VAR growth estimates

I ran vector autoregressive (VAR) models for per capita technology measures and growth across countries a few days ago. These models look like

growth(at time t) = a+ b.growth(t-1) + c.technology change (t-1) + error1
technology change(t) = d+ e.technology change (t-1) + f.growth(t-1) + error2

where a, b, c, d, e, and f are constants. Technology change was measured as per capita change in the number of telephone lines and cell phones.

This plain VAR is a swizz, since the estimates are the same as for OLS, although the standard errors are not as accurate. ARIMA estimation of the same model is not great either, since the exact estimates are usually replaced by the outcomes of numerical optimisation.

Anyway, the estimates of the parameter c are generally negative across countries. I was a bit disappointed at first, as my hypothesis is that greater changes in technology lead to increased growth. But on reflection, the results do not reject the hypothesis. Growth (t-1) and technology change (t-1) are themselves highly correlated, so their two effects are not easily distinguished particularly over short time periods. Furthermore, there is an omitted variable, income, which is correlated with both growth and technology change. However, the correlation is probably far higher with growth usually, so that if growth(t) is small then growth(t-1) is probably small from the omitted variable bias, whereas technology (t-1) is not certain to be small. So growth(t-1) tends to attract a positive bias from the omitted variable, whereas technology gets a negative one.

This argument is roughly right I think but there may be a few caveats and it would better be expressed in mathematical terms.

I had hopes for my VAR estimates on a per country basis, but the two problems mentioned make things difficult. At their heart is the limited number of time periods commonly used in growth regressions, itself caused by the five year averaging in many research approaches including the one above. Adding many other covariates in the model makes the estimates highly uncertain because only five to seven datapoints are available by country, and the estimates in a limited period VAR estimation are perhaps severely biased too. They are probably not even consistent. It is no wonder panel data estimation, for all its faults, has gained ascendancy.